Semi-smooth Newton methods for variational inequalities of the first kind
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 1, pp. 41-62.

Semi-smooth Newton methods are analyzed for a class of variational inequalities in infinite dimensions. It is shown that they are equivalent to certain active set strategies. Global and local super-linear convergence are proved. To overcome the phenomenon of finite speed of propagation of discretized problems a penalty version is used as the basis for a continuation procedure to speed up convergence. The choice of the penalty parameter can be made on the basis of an ${L}^{\infty }$ estimate for the penalized solutions. Unilateral as well as bilateral problems are considered.

DOI: 10.1051/m2an:2003021
Classification: 49J40,  65K10
Keywords: semi-smooth Newton methods, contact problems, variational inequalities, bilateral constraints, superlinear convergence
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title = {Semi-smooth {Newton} methods for variational inequalities of the first kind},
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Ito, Kazufumi; Kunisch, Karl. Semi-smooth Newton methods for variational inequalities of the first kind. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 1, pp. 41-62. doi : 10.1051/m2an:2003021. http://www.numdam.org/articles/10.1051/m2an:2003021/

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